Mining rooted ordered trees under subtree homeomorphism

Mining frequent tree patterns has many applications in different areas such as XML data, bioinformatics and World Wide Web. The crucial step in frequent pattern mining is frequency counting, which involves a matching operator to find occurrences (instances) of a tree pattern in a given collection of trees. A widely used matching operator for tree-structured data is subtree homeomorphism, where an edge in the tree pattern is mapped onto an ancestor-descendant relationship in the given tree. Tree patterns that are frequent under subtree homeomorphism are usually called embedded patterns. In this paper, we present an efficient algorithm for subtree homeomorphism with application to frequent pattern mining. We propose a compact data-structure, called occ, which stores only information about the rightmost paths of occurrences and hence can encode and represent several occurrences of a tree pattern. We then define efficient join operations on the occ data-structure, which help us count occurrences of tree patterns according to occurrences of their proper subtrees. Based on the proposed subtree homeomorphism method, we develop an effective pattern mining algorithm, called TPMiner. We evaluate the efficiency of TPMiner on several real-world and synthetic datasets. Our extensive experiments confirm that TPMiner always outperforms well-known existing algorithms, and in several cases the improvement with respect to existing algorithms is significant.     

Problem reduction representation for the linguistic analysis of waveforms

This paper shows how the nondirectional structural analysis of pattern data can be performed by matching a problem reduction representation (PRR) of pattern structure with sample data, using a best-first state space search algorithm called SSS*. The end result of the matching algorithm is a tree whose nodes represent recognized structures in the data. Tip nodes of the tree structure correspond to primitives which are recognized in the raw data by curve fitting routines. The operators of the algorithm allow the tree to be constructed with a combination of top-down or bottom-up steps. The matching of the structure tree to waveform segments need not be done in a left-right sequence. Moreover ambiguous matches are pursued in a best first order by using state space search with partial parse trees as states. A software system called WAPSYS (for waveform parsing system) is described, which implements this structural analysis paradigm. Experience using WAPSYS to analyze carotid pulse waves is also discussed.     

基于后缀树的带有通配符的模式匹配研究

由于在生物序列分析、文本索引、网络入侵检测等领域的应用需求,带有通配符的模式匹配问题一直是研究 的热点。针对已有的研究工作中通配符和长度约束具有较强的局限性问题,研究带有灵活通配符的模式匹配问题,其 中通配符可以在模式的任意两子串间出现且可以指定灵活的长度约束。采用非线性数据结构—后缀树,设计了求 解模式所有解的完备算法PAS"I'。预处理阶段采用在线增量式算法构建具有文本先验知识的后缀树,搜索阶段结合 动态规划的思想,逐个匹配模式中字符,最终得到完备解。在基因序列上的实验表明,PAST比其他算法具有更好的 时间性能。     

面向中英文混合环境的多模式匹配算法

分析了中英文混合环境下多模式匹配的特点,以及已有多模式匹配算法应用于中英文混合环境时的不足,给出并证明了中英文混合环境下多模式匹配算法的性能定理,提出了一种适合于中英文混合环境的基于线索完全哈希Trie结构的多模式匹配算法.该算法扩展了标准Trie结构,以中英文字符内码为键值构造完全哈希Trie匹配机,并利用模式串之间的关系对Trie匹配机进行线索化.理论分析与实验结果表明,所提出的算法在匹配中无需复杂的哈希运算,不需要回溯匹配指针,在中英文混合环境下能够进行正确、高效的匹配,而且不存在空间膨胀问题,具有较低的空间与时间复杂度,有较大理论与应用价值.     

Tree pattern query minimization

Tree patterns form a natural basis to query tree-structured data such as XML and LDAP. To improve the efficiency of tree pattern matching, it is essential to quickly identify and eliminate redundant nodes in the pattern. In this paper, we study tree pattern minimization both in the absence and in the presence of integrity constraints (ICs) on the underlying tree-structured database. In the absence of ICs, we develop a polynomial-time query minimization algorithm called CIM, whose efficiency stems from two key properties: (i) a node cannot be redundant unless its children are; and (ii) the order of elimination of redundant nodes is immaterial. When ICs are considered for minimization, we develop a technique for query minimization based on three fundamental operations: augmentation (an adaptation of the well-known chase procedure), minimization (based on homomorphism techniques), and reduction. We show the surprising result that the algorithm, referred to as ACIM, obtained by first augmenting the tree pattern using ICs, and then applying CIM, always finds the unique minimal equivalent query. While ACIM is polynomial time, it can be expensive in practice because of its inherent non-locality. We then present a fast algorithm, CDM, that identifies and eliminates local redundancies due to ICs, based on propagating "information labels" up the tree pattern. CDM can be applied prior to ACIM for improving the minimization efficiency. We complement our analytical results with an experimental study that shows the effectiveness of our tree pattern minimization techniques.     

Optimal prefix and suffix queries on texts

In this paper, we study a restricted version of the position restricted pattern matching problem introduced and studied by Mäkinen and Navarro [V. Mäkinen, G. Navarro, Position-restricted substring searching, in: J.R. Correa, A. Hevia, M.A. Kiwi (Eds.), LATIN, in: Lecture Notes in Computer Science, vol. 3887, Springer, 2006, pp. 703-714]. In the problem handled in this paper, we are interested in those occurrences of the pattern that lies in a suffix or in a prefix of the given text. We achieve optimal query time for our problem against a data structure which is an extension of the classic suffix tree data structure. The time and space complexity of the data structure is dominated by that of the suffix tree. Notably, the (best) algorithm by Mäkinen and Navarro, if applied to our problem, gives sub-optimal query time and the corresponding data structure also requires more time and space.     

Efficiently mining frequent trees in a forest: algorithms and applications

Mining frequent trees is very useful in domains like bioinformatics, Web mining, mining semistructured data, etc. We formulate the problem of mining (embedded) subtrees in a forest of rooted, labeled, and ordered trees. We present TREEMINER, a novel algorithm to discover all frequent subtrees in a forest, using a new data structure called scope-list. We contrast TREEMINER with a pattern matching tree mining algorithm (PATTERNMATCHER), and we also compare it with TREEMINERD, which counts only distinct occurrences of a pattern. We conduct detailed experiments to test the performance and scalability of these methods. We also use tree mining to analyze RNA structure and phylogenetics data sets from bioinformatics domain.     

WSM: a novel algorithm for subgraph matching in large weighted graphs

Given an undirected/directed large weighted data graph and a similar smaller weighted pattern graph, the problem of weighted subgraph matching is to find a mapping of the nodes in the pattern graph to a subset of nodes in the data graph such that the sum of edge weight differences is minimum. Biological interaction networks such as protein-protein interaction networks and molecular pathways are often modeled as weighted graphs in order to account for the high false positive rate occurring intrinsically during the detection process of the interactions. Nonetheless, complex biological problems such as disease gene prioritization and conserved phylogenetic tree construction largely depend on the similarity calculation among the networks. Although several existing methods provide efficient methods for graph and subgraph similarity measurement, they produce nonintuitive results due to the underlying unweighted graph model assumption. Moreover, very few algorithms exist for weighted graph matching that are applicable with the restriction that the data and pattern graph sizes are equal. In this paper, we introduce a novel algorithm for weighted subgraph matching which can effectively be applied to directed/undirected weighted subgraph matching. Experimental results demonstrate the superiority and relative scalability of the algorithm over available state of the art methods.     

Homeomorphic alignment of weighted trees

Motion capture, a currently active research area, needs estimation of the pose of the subject. For this purpose, we match the tree representation of the skeleton of the 3D shape to a pre-specified tree model. Unfortunately, the tree representation can contain vertices that split limbs in multiple parts, which do not allow a good match by usual methods. To solve this problem, we propose a new alignment, taking into account the homeomorphism between trees, rather than the isomorphism, as in prior works. Then, we develop several computationally efficient algorithms for reaching real-time motion capture.     

The directed subgraph homeomorphism problem

The set of pattern graphs for which the fixed directed subgraph homeomorphism problem is NP-complete is characterized. A polynomial time algorithm is given for the remaining cases. The restricted problem where the input graph is a directed acyclic graph is in polynomial time for all pattern graphs and an algorithm is given.     

Parameterized point pattern matching and its application torecognition of object families

The problem of recognizing and localizing objects that can vary in parameterized ways is considered. To achieve this goal, a concept of parameterized point pattern is introduced to model parameterized families of such objects, and a parameterized point pattern matching algorithm is proposed. A parameterized point pattern is a very flexible concept that can be used to model a large class of parameterized objects, such as a pair of scissors with rotating blades. The proposed matching algorithm is formulated as a tree search procedure, and it generates all maximum matchings satisfying a condition called δ-boundedness. Several pruning methods based on the condition of δ-boundedness and their efficient computing techniques are given. The proposed matching algorithm is applied to a real shape matching problem in order to check the validity of the approach     

EPMA: Efficient pattern matching algorithm for DNA sequences

To solve, manage and analyze biological problems using computer technology is called bioinformatics. With the emergent evolution in computing era, the volume of biological data has increased significantly. These large amounts of data have increased the need to analyze it in reasonable space and time. DNA sequences contain basic information of species, and pattern matching between different species is an important and challenging issue to cope with. There exist generalized string matching and some specialized DNA pattern matching algorithms in the literature. There is still need to develop fast and space efficient pattern matching algorithms that consider new hardware development. In this paper, we present a novel DNA sequences pattern matching algorithm called EPMA. The proposed algorithm utilizes fixed length 2-bits binary encoding, segmentation and multi-threading. The idea is to find the pattern with multiple searcher agents concurrently. The proposed algorithm is validated with comparative experimental results. The results show that the new algorithm is a good candidate for DNA sequence pattern matching applications. The algorithm effectively utilizes modern hardware and will help researchers in the sequence alignment, short read error correction, phylogenetic inference etc. Furthermore, the proposed method can be extended to generalized string matching and their applications.     

Structure and Recognition of Graphs with No 6-wheel Subdivision

The subgraph homeomorphism problem has been shown by Robertson and Seymour to be polynomial-time solvable for any fixed pattern graph H. The result, however, is not practical, involving constants that are worse than exponential in |H|. Practical algorithms have only been developed for a few specific pattern graphs, the most recent of these being the wheels with four and five spokes. This paper looks at the subgraph homeomorphism problem where the pattern graph is a wheel with six spokes. The main result is a theorem characterizing graphs that do not contain subdivisions of W ₆. We give an efficient algorithm for solving the subgraph homeomorphism problem for W ₆. We also give a strengthening of the previous W ₅ result.     

Graphical models and point pattern matching

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.     

基于有序二叉树的多模式匹配算法

一、简介在一个文本串中查找用户指定的模式串在信息抽取和文本编辑中有着广泛的应用。当前,有限状态自动机(DFSA)算法是解决多模式匹配问题的常用方法。DFSA算法在匹配前对模式串集合进行预处理,转换成树型有限状态自动机,然后只需对文本串进行一次扫描就可找出所有模式串,其查找时间复杂度是O(n)。后来,在这个算法的基础上又有一些改进,实现了跳跃式查找。基于树型结构的有限自动机特别适     

Web信息抽取中基于结点权重的树编辑距离匹配法研究

提出一种改进的树匹配算法,通过考量HTML特性,对树编辑距离方法进行改进,根据不同HTML树结点在浏览器中所显示的相关数据的不同权重赋以不同的权重值。算法由HTML数据对象构造具有结点权重的HTML树,模式识别通过取得两棵构造树的最大映射值达成。通过基于商用网站的实验对算法有效性进行了证实。     

一种并行中英文混合多模式匹配算法

针对中英文混合文本的匹配准确性及大规模数据文本的匹配效率等问题,基于经典的线索化完全哈希特里树算法,提出一种并行化的中英文混合多模式文本匹配算法。采用拆分文本降低多模式匹配算法的串行度,进而在拆分出的小文本上并行地执行文本匹配。通过并行化预处理过程,设计新的存储结构。实验结果表明,该算法在保证结果正确的前提下,执行效率高于经典的串行匹配算法,当数据规模达到226个字符时,可以获得8倍以上的加速比。     

一种基于可排序视图的RDF模式匹配算法

随着语义网络中数据量的激增,在RDF数据集中高效查询数据已成为一个亟待解决的问题。传统的基于物化视图的RDF模式匹配方法虽然能降低表的自连接操作次数,加快查询模式重写过程,但在视图集中检索模式匹配的视图等价于子图同构这一NP-hard问题。为了减小查询模式重写代价,提高RDF模式匹配过程效率,引入可排序视图概念,设计包含映射发现算法contain及其扩展算法contain+,简化等长度模式间包含映射发现过程,同时保证模式间的匹配代价与输入数据的规模线性相关。此外,提出基于倒排表/MapReduce检索候选可排序视图的方法,实现RDF模式重写算法rewrite,用以处理不同规模数据集上的模式匹配问题。理论分析及实验证明,基于可排序视图的RDF模式匹配算法能有效地兼顾算法效率及算法可扩展性。     

StringB-tree在软件复用中的应用研究

提出了将StringB-tree用于解决软件复用中的参数化样式匹配问题(parameterizedpatternmatching)。通过对参数化字符串做一个变换,使用StringB-tree这种特殊的数据结构可提高匹配效率。文章的重点有两部分,一个是介绍了StringB-tree这种特殊的数据结构的优点及其构建过程;另一个是讲怎样利用StringB-tree解决参数化样式匹配问题。